Formal Methods and Agent-Based Systems

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Formal Methods and Agent-Based Systems

Michael Luck and Mark dInverno

1.1 Introduction

As has been discussed elsewhere [17], much agent-related work has tended to focuson either the development of practical applications, or the development of sophisti-

cated logics for reasoning about agents. Our own view is that work on formal models

of agent-based systems is valuable inasmuch as they contribute to a fundamental goal

of computing to build real agent systems. This is not to trivialise or denigrate the ef-

fort of formal approaches, but to direct them towards integration in a broader research

programme. In an ongoing project that has been running for several years, we have

sought to do exactly that through the development of a formal framework, known as

SMART, that provides a conceptual infrastructure for the analysis and modelling of

agents and multi-agent systems on the one hand, and enables implemented and de-

ployed systems to be evaluated and compared on the other. In this paper, we describe

our research programme, review its achievements to date, and suggest directions for

the future.

In particular, we consider the role of autonomy in interaction. Autonomy is in-

dependence; it is a state that does not rely on any external entity for purposeful

existence. In this paper, we use our existing agent framework to address the issues

that arise in a consideration of autonomous interaction. We begin by considering sev-

eral problems that are prevalent in existing models of interaction, and which must be

addressed in attempting to construct a model of autonomous interaction. Then we

introduce a previously developed agent framework on which the remainder of the

paper is based. The next sections describe and specify an autonomous social agent

that acts in an environment, the way in which it generates its goals, and finally how

it interacts with others in its environment. We discuss how this can be viewed as a

process of discovery, and what such a view usefully brings to the problem.

1.1.1 Theory and Practice

Though the fragmentation into theoretical and practical aspects has been noted, and

several efforts made in attempting to address this fragmentation in related areas of


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2 Formal Approaches to Agent-based Systems

agent-oriented systems by, for example, [14], [22], and [32], much remains to be

done in bringing together the two strands of work.

This section draws on Lucks outline [17] of the ways in which some progress

has been made with BDI agents, a well-known and effective agent architecture. Rao,

in particular, has attempted to unite BDI theory and practice in two ways. First, heprovided an abstract agent architecture that serves as an idealization of an imple-

mented system and as a means for investigating theoretical properties [28]. Second,

he took an alternative approach by starting with an implemented system and then

formalizing the operational semantics in an agent language, AgentSpeak(L), which

can be viewed as an abstraction of the implemented system, and which allows agent

programs to be written and interpreted [27].

In contrast to this approach, some work aims at constructing directly executable

formal models. For example, Fishers work on Concurrent MetateM [11] has at-

tempted to use temporal logic to represent individual agent behaviours where the

representations can either be executed directly, verified with respect to a logical re-

quirement, or transformed into a more refined representation. Further work aims to

use this to produce a full development framework from a single high-level agent toa cooperating multi-agent system. In a similar vein, [25] aims to address the gap be-

tween specification and implementation of agent architectures by viewing an agent

as a multi-context system in which each architectural component is represented as a

separate unit, an encapsulated set of axioms, and an associated deductive mechanism

whose interrelationships are specified using bridge rules. Since theorem-provers al-

ready exist for multi-context systems, agents specified in this way can also be directly

executed.

As yet, the body of work aimed at bridging the gap between theory and practice

is small. Fortunately, though, there seems to be a general recognition that one of

the key roles of theoretical and practical work is to inform the other [8], and while

this is made difficult by the almost breakneck pace of progress in the agent field,

that recognition bodes well for the future. Some skeptics remain, however, such as

Nwana, who followed Russell in warning against premature mathematization, and

the danger that lies in wait for agent research [4].

1.1.2 General Approach

As stated above, we view our enterprise as that of building programs. In order to

do so, however, we need to consider issues at different points along what we call

the agent development line, identifying the various foci of research in agent-based

systems in support of final deployment, as shown in Figure 1.1. To date, our work

has concentrated on the first three of the stages identified.

We have provided a formal agent framework within which we can explore some

fundamental questions relating to agent architectures, configurations of multi-agent systems, inter-agent relationships, and so on, independent of any particular

model. The framework continues to be extended to cover a broader range of

issues, and to provide a more complete and coherent conceptual infrastructure.


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1 Formal Methods and Agent-Based Systems 3

In contrast to starting with an abstract framework and refining it down to par-ticular system implementations, we have also attempted to start with specific

deployed systems and provide formal analyses of them. In this way, we seek to

move backwards to link the system specifications to the conceptual formal frame-

work, and also to provide a means of comparing and evaluating competing agentsystems.

The third strand aims to investigate the process of moving from the abstract tothe concrete, through the construction of agent development methodology, an

area that has begun to receive increasing attention. In this way, we hope to marry

the value of formal analysis with the imperative of systems development in a

coherent fashion, leading naturally to the final stage of the development line, to

agent deployment.

Agent Framework

Agent Deployment

Agent Development

Agent Systems Specification

Fig. 1.1.The Agent Development Line.

This paper can be seen as an extension of the work contained in [21], which

describes the results of the research programme in providing a foundation for the

exploration of more advanced issues in agent-based systems. That work introduced

requirements for formal frameworks, and showed how our agent framework satisfied

those requirements in relation to, for example, some initial inter-agent relationships,

and their application to the Contract Net Protocol. In this paper, we build on that

work, showing further levels of analysis of agent relationships, and also describe

further work on formal agent specification.In what follows, we use the Z specification language [31] , for reasons of acces-

sibility, clarity and existing use in software development. The arguments are well-

rehearsed and can be found in many of the references given at the end of the paper.


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Here, we present a brief introduction to the language but more details can be found

in an array of text books such as [31]. The specification in this paper is not intended

to be complete, nor to provide the most coherent exposition of a particular piece of

work, but to show how a broad research programme in support of the aims above is

progressing. Details of the different threads of work may be found in the referencesin each of the relevant sections. In particular, this paper is concerned with the design

ofautonomous agents: what it means for an agent to be autonomous and what that

entails for any adequate model of interaction between such agents. Complex envi-

ronments admit an inherent uncertainty that must be considered if we are to cope

with more than just toy problems. In such uncertain environments, an agent must

be autonomous; an agent cannot know in advance the exact effects of its or others

actions. This is of paramount importance, and an agent must therefore be designed

with a flexibility that enables it to cope with this uncertainty by evaluating it and

responding to it in adequate ways.

1.1.3 Introduction to Z

The formal specification language, Z, is based on set theory and first order predicate

calculus. It extends the use of these languages by allowing an additional mathemati-

cal type known as theschema type. Z schemas have two parts: the upper declarative

part, which declares variables and their types, and the lower predicate part, which

relates and constrains those variables. The type of any schema can be considered

as the Cartesian product of the types of each of its variables, without any notion of

order, but constrained by the schemas predicates.

It is therefore appropriate to liken the semantics of a schema to that of Cartesian

products. For example, suppose we define a schema as follows.

Pair

first: Nsecond: N

This is very similar to the following Cartesian product type.

Pair== N N

The difference between these forms is that there is no notion of order in the

variables of the schema type. In addition, a schema may have a predicate part that

can be used to constrain the state variables. Thus, we can state that the variable, first,

can never be greater than second.

Pair

first: Nsecond: N

first second


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Modularity is facilitated in Z by allowing schemas to be included within other

schemas. We can select a state variable, var, of a schema, schema, by writing

schema.var. For example, it should be clear thatPair.firstrefers to the variable first

in the schemaPair.

Now, operations in a state-based specification language are defined in terms ofchanges to the state. Specifically, an operation relates variables of the state after the

operation (denoted by dashed variables) to the value of the variables before the oper-

ation (denoted by undashed variables). Operations may also have inputs (denoted by

variables with question marks), outputs (exclamation marks) and preconditions. In

theGettingCloserschema below, there is an operation with an input variable, new?;ifnew?lies between the variables firstandsecond, then the value offirstis replacedwith the value ofnew?. The value ofseconddoes not change, and the output old!is equal to the value of the variable firstas it was before the operation occurs. The

Pairsymbol, is an abbreviation forPair Pair and, as such, includes in the oper-ation schema all the variables and predicates of the state ofPairbefore and after the

operation.

GettingCloser

new? : NPair

old! : N

first new?new? second

first =new?second =secondold! =first

To introduce a type in Z, where we wish to abstract away from the actual content

of elements of the type, we use the notion of a given set. For example, we write[NODE] to represent the set of all nodes. If we wish to state that a variable takeson some set of values or an ordered pair of values we write x : PNODE and x :

NODENODE, respectively. Arelationtype expresses some relationship betweentwo existing types, known as the sourceandtargettypes. The type of a relation with

source Xand target Y is P(X Y). A relation is therefore a set of ordered pairs.When no element from the source type can be related to two or more elements from

the target type, the relation is a function. A totalfunction () is one for which everyelement in the source set is related, while a partial function ( ) is one for whichnot every element in the source is related. A sequence (seq) is a special type of

function where the domain is the contiguous set of numbers from 1 up to the number

of elements in the sequence. For example, the first relation below defines a function

between nodes, while the second defines asequenceof nodes.

Rel1 ={(n1, n2), (n2, n3), (n3, n2)}Rel2 ={(2, n3), (3, n2), (1, n4)}


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In Z, a sequence is more usually written as n4, n3, n2. The domain (dom) ofa relation or function comprises those elements in the source set that are related,

and the range (ran) comprises those elements in the target set that are related. In

the examples above, domRel1 = {n1, n2, n3}, ranRel1 = {n2, n3}, domRel2 =

{1, 2, 3} and ranRel2 = {n2, n3, n4}. Sets of elements can be defined using setcomprehension. For example, the following expression denotes the set of squares of

natural numbers greater than10 : {x: N | x > 10 x x}.For a more complete treatment of the Z language, the interested reader is referred

to one of the numerous texts, such as [31].

1.2 Autonomous Interaction

Autonomy allows the design of agents to be flexible enough to function effectively

and efficiently in a sophisticated world [5]. Typically, real autonomy has been ne-

glected in most research. We hear of benevolent, altruistic, trusting, sympathetic

or cooperative agents, yet a truly autonomous agent will behave only in a selfishway. Cooperation, for example, should occur only as a consequence of an agents

selfish motivations (which might of course include motivations relating to social ac-

ceptance that would drive what appears at face value to be social or altruistic

behaviour). Autonomy allows for no artificially imposed rules of behaviour; all be-

haviour must be a consequence of the understanding and processing capabilities of

that agent. Modelling this fundamental notion of selfish behaviour and the generation

of goals by such a selfish autonomous agent is of vital importance in the design of

autonomous agents.

In multi-agent systems, the interactions between agents are the basis for usefully

exploiting the capabilities of others. However, such a pragmatic approach has not

been the concern of many researchers who instead often focus on small areas of

interaction and communication, and in particular on specialised forms of intention

recognition and interpretation.

In many existing models of interaction, agents are not autonomous. In consid-

ering these models, we can identify problem-issues in autonomous interaction. Our

intention is simply to show why these models are not adequate for autonomous in-

teraction, and so isolate problems which contribute to the non-autonomous nature of

these models.

Pre-determined Agenda Problem-solving can be considered to be the task of find-

ing actions that achieve current goals. Typically, goals have been presented to

systems without regard to the problem-solving agent so that the process is di-

vorced from the reality of an agent in the world. This is inadequate for models

of autonomy which require an understanding of how such goals are generated

and adopted. Surprisingly, however, this is an issue which has received very lit-tle attention with only a few notable exceptions (e.g. [24]).

Benevolence In traditional models of goal adoption, goals are broadcast by one

agent, and adopted by other agents according to their own relevant compe-


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tence [30]. This assumes that agents are already designed with common or non-

conflicting goals that facilitate the possibility of helping each other satisfy ad-

ditional goals. Negotiation as to how these additional goals are satisfied typi-

cally takes the form of mere goal-node allocation. Thus an agent simply has to

communicate its goal to another agent for cooperation in the form of joint plan-ning to ensue. The concept of benevolence that agents will cooperate with

other agents whenever and wherever possible has no place in modelling au-

tonomous agents [7, 12]. Cooperation will occur between two parties only when

it is considered advantageous to each party to do so. Autonomous agents are

thus selfish agents. A goal (whether traditionally viewed as selfish or altruis-

tic) will always be adopted so as to satisfy a selfish motivation.

Guaranteed Effects Speech Act Theory (SAT) [3, 29] underlies

much existing work in AI [6], typically because as Appelt points out, speech

acts are categorizable and can be modelled as action operators in a planning

environment [2]. However, this work admits a serious flaw. Although the pre-

conditions of these operators are formulated in terms of the understanding of the

planning agent, the post-conditions or effects of these operators do not updatethe understanding of the planning agent, but of the agent at whom the action is

directed [1]. No agent can ever actually knowwith any certainty anything about

the effects of an action, whether communicative or otherwise. It is only through

an understanding of the targetagent and through observing the future behaviour

of that agent, that the agent can discover the actual effects of the interaction. This

uncertainty is inherent in communication between autonomous agents and must

be a feature of any model of interaction which hopes to reflect this reality.

Automatic Intention Recognition A related though distinct problem with using

SAT in the design ofcommunicationmodels involves the notion that the mean-

ing of an utterance is a function of the linguistic content of that utterance. SAT is

unable (even when one tries to force rather undistinguished ad-hoc rules [15]) to

model any kind of utterance where the linguistic content is not very close to the

speakers intended meaning. That is to say that the operators themselves are con-

text independent, and information about how context affects the interpretation

of utterances is not explicitly captured. Communication varies from utterances

with a meaning identical to linguistic content through utterances which have a

meaning opposite to the linguistic content to utterances where the meaning does

not seem to be categorised at all by the linguistic content. In short, Speech Act

Theory cannot lead to a model of autonomous interaction. It merely serves to

describe a very limiting case of linguistic communication at a suitable level for

planning operators. A more flexible account of how intention is recovered from

a multitude of different utterances is required.

Multi-Agent Modelling This is also a related but more subtle problem. Much work

has modelled communicative actions in terms of mutual beliefs about the op-

erator and its known effects [26]. This proposes to show not only how certainmental states lead to speech actions, but how speech actions affect mental states.

We argue that any account of autonomous interaction should only model the ef-


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fects of an action upon the mental state of the agent initiating the interaction (or

another single agent).

In summary, there are several important claims here: first, an agent cannot be

truly autonomous if its goals are provided by external sources; second, an agent willonly adopt a goal and thus engage in an interaction if it is to its advantage to do

so; third, the effects of an interaction cannot be guaranteed; fourth, the intentions of

others cannot always be recognised; fifth, an agent can only know about itself.

Note that the first claim requires goals to be generated from within. It is this

internal goal generation that demands an explicit model of the motivations of the

agent. The second claim requires a notion of advantage that can only be determined

in relation to the motivations of the agent. The third and fourth claims demand that

the uncertain nature of autonomous interaction be explicitly addressed. We argue that

viewing autonomous interaction as motivated discovery provides us with a means

for doing this. Finally, the fifth claim imposes constraints on the problem we are

considering, and provides a strong justification for our concern with constructing a

model of autonomous interaction from the perspective of an individual agent.

1.3 The Formal Agent Framework

We begin by briefly reviewing earlier work. In short, we propose a four-tiered hierar-

chy comprising entities, objects, agents and autonomous

agents [18]. The basic idea underlying this hierarchy is that all components of the

world are entities. Of these entities, some are objects, of which some, in turn, are

agents and of these, some are autonomous agents, as shown in Figure 1.2.

Neutral Objects

Server Agents

Agents

Autonomous

Agents

Objects

Entities

Fig. 1.2.The Entity Hierarchy.


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Before it is possible to construct agent models it is necessary to define the build-

ing blocks or primitives from which these models are created. We start by defining

three primitives:attributes,actionsand motivations, which are used as the basis for

development of theSMARTagent framework. Formally, these primitives are specified

as given sets which means that we say nothing about how they might be representedfor any particular system. In addition, two secondary concepts, goals and environ-

ments, are specified in terms of attributes.

Attributes are simply features of the world, and are the only characteristics that

are manifest. They need not be perceived by any particular entity, but must be po-

tentially perceivable in an omniscient sense. This notion of a feature allows anything

to be included such as, for example, the fact that a tree is green, or is in a park, or

is twenty feet tall. An environment is then simply a set of attributes that describes

allthe features within that environment. Thus a type,Environment, is defined to be a

(non-empty) set of attributes. The second primitive that needs defining is an action.

Actions can change environments by adding or removing attributes. For example,

the action of a robot, responsible for attaching tyres to cars in a factory, moving from

one wheel to the next, will delete the attribute that the robot is at the first wheel andadd the attribute that the agent is at the second. A goal defines a state of affairs that

is desirable in some way. For example, a robot may have the goal of attaching a tyre

to a car. A goal can therefore be very simply defined as a non-empty set of attributes

that describes a state of affairs in the world. Lastly,motivations can be introduced.

A motivation is any desire or preference that can lead to the generation and adoption

of goals and that affects the outcome of the reasoning or behavioural task intended

to satisfy those goals.

In summary we have the following definitions, from which we can construct

an entity that has a non-empty set of attributes, and is therefore perceivable. For

example, a goal is defined as a non-empty set of attributes.

[Attribute,Action,Motivation]

Environment== P1

Attribute

Goal== P1

Attribute

Entity

attributes: PAttributecapabilities: PActiongoals: P Goalmotivations: PMotivation

attributes={ }

1.3.1 Objects

Entities able to affect their environment through action lead to the concept ofobjects.

An object in our model is an entity with capabilities. TheObjectschema below has


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a declarative part that simply includes the previously defined schema, Entity. The

predicate part of the schema specifies that an object must have a non-empty set of

actions as well as attributes. Objects are therefore defined by their ability in terms of

their actions, and their characteristics in terms of their attributes.

Object

Entity

capabilities={ }

Since an object has actions, these may be performed in certain environments that

will be determined by the state of that environment. The behaviour of an object can

therefore be modelled as a mapping from the environment to a set of actions that are

a subset of its capabilities. This mapping is known as the action-selectionfunction.

The variable,willdo, specifies the next actions that the object will perform. Its value

is found by applying theobjectactionsfunction to the current environment, in which

it is situated.

ObjectState

Object

objectactions: Environment PActionwilldo: PActionenvironment: Environment

willdo= objectactions environment

Aninteractionwith the environment occurs as a result of performing actions in it.

Its effects on the environment are determined by applying the effectinteractfunction

in the axiom definition below to the current environment and the actions taken.

effectinteract: Environment PAction Environment

1.3.2 Agents and Autonomy

An agent is then just an object either that is useful to another agent where this useful-

ness is defined in terms of satisfying that agents goals, or that exhibits independent

purposeful behaviour. In other words, an agent is an object with an associated set of

goals. This definition of agents relies on the existence of other agents that provide

the goals that are adopted in order to instantiate an agent. In order to escape an in-

finite regress of goal adoption, we define autonomous agents, which are agents that

generate their own goals from motivations.

AgentObject

goals={ }


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AutonomousAgent

Agent

motivations={ }

For completeness we also define neutral objects as those objects that are not

agents, and server agents as those agents that are not autonomous.

NeutralObject

Object

goals= {}

ServerAgent

Object

motivations= {}

1.3.3 Autonomous Perception

An agent in an environment can perceive certain attributes subject to its capabilities

and current state but, due to limited resources, may not be able to perceive all at-

tributes. The action of an agent is based on a subset of attributes of the environment,

the agentsactualpercepts.

To distinguish between representations of mental models and representations of

the actual environment, a type, View, is defined to be the perception of an envi-

ronment by an agent. This has an equivalent type to that ofEnvironment, but now

physical and mental components of the same type can be distinguished.

View== P1

Attribute

An autonomous agent has a (possibly empty) set of actions that enable it to per-

ceive its world, which we call its perceiving actions. The set of percepts that an

autonomous agent is potentially capable of perceiving is a function of the current

environment, which includes the agents situation and its perceiving actions. Since

the agent is resource-bounded, it may not be able to perceive the entire set of at-

tributes and selects a subset based on its current goals. For example, the distributed

Multi-Agent Reasoning System (dMARS) [10], may have a set of events to process,

where events correspond to environmental change. Each of these percepts (or events)

is available to the agent but because of its limited resources it may only be able to

process one event, and must make a selection based on its goals.

The perception capabilities of an agent are defined in the schema below,AutonomousAgentPerception,

which includes theAutonomousAgentschema and refines it by introducing three vari-

ables. First, the set of perceiving actions is denoted by perceivingactions, a subset of


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the capabilities of an autonomous agent. Thecanperceivefunction determines the at-

tributes that are potentially available to an agent through its perception capabilities.

Notice that this function is applied to a physical environment (in which it is situated)

and returns a mental environment. The second argument of this schema is constrained

to be equal to perceivingactions. Finally, the function, willperceive, describes thoseattributes actually perceived by an agent. This function is always applied to the moti-

vations and goals of the agent and in contrast to the previous function, takes a mental

environment and returns another mental environment.

AutonomousAgentPerception

AutonomousAgent

perceivingactions: PActioncanperceive : Environment PAction Viewwillperceive : PMotivation P Goal View View

perceivingactions capabilities e: Environment; as: PAction

as dom(canperceive e) as = perceivingactions

To specify the actions of an autonomous agent, the next schema includes the

AutonomousAgentschema and then defines an action-selection function that is de-

termined in relation to the motivations, goals, perceived environment and actual en-

vironment of the agent. This function gives the set of actions the agent will perform,

in order to achieve some goal. The physical environment is important here as it de-

termines the action that is actually performed by the agent as opposed to the action

which is intended (or selected) by the agent. These will not be the same in all cases

as the agent may, for example, have incomplete or incorrect perceptions of its envi-

ronment.

AutonomousAgentActAutonomousAgent

autoactions: PMotivation P Goal ViewEnvironment PAction

Now, we need to define the state of an agent as follows by including the pre-

vious schemas and the current environment, and introducing variables for possible

percepts, posspercepts, actual percepts, actualpercepts, and the actions performed,

willdo.


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AutonomousAgentState

ObjectState

AutonomousAgentPerception

AutonomousAgentAct

env: Environmentposspercepts, actualpercepts : Viewwilldo: PAction

actualpercepts possperceptsposspercepts= canperceive env perceivingactionsactualpercepts = willperceive motivations goals possperceptswilldo= autoactions motivations goals actualpercepts env

1.3.4 Goal Generation

As stated above, in order for an agent to be autonomous, it must generate goalsfrom

motivations. The initial point in any interaction is when this goal generation processoccurs. In this section, we describe how an autonomous agent, definedin terms of its

somewhat abstractmotivations, can construct goals or concrete states of affairs to be

achieved in the environment. Our model requires a repository of known goals which

capture knowledge of limited and well-defined aspects of the world. These goals

describe particular states or sub-states of the world with each autonomous agent

having its own such repository. An agent tries to find a way to mitigate motivations

by selecting an action to achieve an existing goal or by retrieving a goal from a

repository of known goals, as considered below.

In order to retrieve goals to mitigate motivations, an autonomous agent must

have some way of assessing the effects of competing or alternative goals. Clearly,

the goals that make the greatest positive contribution to the motivations of the agent

should be selected. The GenerateGoal schema below describes at a high level anautonomous agent monitoring its motivations for goal generation. First, as indicated

by AutonomousAgent, the sociological agent changes, and a new variable repre-

senting the repository of available known goals, goalbase, is declared. Then, the

motivational effect on an autonomous agent of satisfying a set of new goals is given.

Themotiveffectfunction returns a numeric value representing the motivational effect

of satisfying a set of goals with a particular configuration of motivations and a set

of existing goals. The predicate part specifies all goals currently being pursued must

be known goals that already exist in the goalbase. Finally, there is a set of goals in

the goalbase that has a greater motivational effect than any other set of goals, and the

current goals of the agent are updated to include the new goals.


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GenerateGoal

AutonomousAgent

goalbase: P Goalmotiveffect: PMotivation P Goal P Goal Z

goals goalbase goals goalbase gs: P Goal| gs goalbase

( os: P Goal| os (P goalbase)(motiveffect motivations goals gs

motiveffect motivations goals os)goals =goals gs)

1.4 Inter-Agent Relationships

Agents and autonomous agents are thus defined in terms of goals. Agents satisfy

goals, while autonomous agents may, additionally, generate them. Goals may beadopted by either autonomous agents, non-autonomous agents or objects without

goals. Since non-autonomous agents satisfy goals for others theyrelyon other agents

for purposeful existence, indicating that goal adoption creates critical inter-agent re-

lationships.

A direct engagement takes place whenever a neutral-object or a server-agent

adopts the goals of another. Thus, an agent with some goals, called the client, uses

another agent, called theserver, to assist them in the achievement of those goals.

DirectEngagement

client: Agentserver: ServerAgentgoal: Goal

client=servergoal (client.goals server.goals)

Once autonomous agents have generated goals and engaged other server-agents,

these server-agents may, in turn, engage other non-autonomous entities with the pur-

pose of achieving or pursuing the original goal. This process can then, in princi-

ple, continue indefinitely. An engagement chainthus represents the goal and all the

agents involved in the sequence of direct engagements. Since goals are grounded by

motivations, the agent at the head of the chain must be autonomous.


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EngagementChain

goal: Goalautonomousagent: AutonomousAgentagentchain : seq ServerAgent

#agentchain > 0goal autonomousagent.goalsgoal

{s: ServerAgent| s ran agentchain s.goals}

A cooperation describes a goal, the autonomous agent that generated the goal,

and those autonomous agents that have adopted that goal from the generating agent.

In addition, all the agents involved have the goal of the cooperation, an agent cannot

cooperate with itself, and the set of cooperating agents must be non-empty. Coopera-

tion cannot, therefore, occur unwittingly between agents, but must arise as a result of

the motivations of an agent and the agent recognising that goal in another. (The defi-

nition below does not capture the notion of this recognition and adoption but simply

provides an abstract template which could be further elaborated as required.)

Cooperation

goal: Goal; generatingagent: AutonomousAgentcooperatingagents: PAutonomousAgent

goal generatingagent.goals aa: cooperatingagents goal aa.goalsgeneratingagentcooperatingagentscooperatingagents={ }

The key relationships in a multi-agent system are direct engagements, engage-

ment chains and cooperations [19]. The combined total of direct engagements, en-

gagement chains and cooperations (represented as dengagements, engchains andcooperations) defines a social organisation that is not artificially or externally im-

posed but arises as a natural and elegant consequence of our definitions of agents

and autonomous agents. This organisation is defined in the AgentSocietyschema be-

low.

AgentSociety

entities: PEntityobjects: P Objectagents : PAgentautonomousagents: PAutonomousAgentdengagements: PDirectEngagementengchains: PEngagementChain

cooperations: P Cooperation

By considering the entire set of engagements, engagement chains and coopera-

tions, a map of the relationships between individual agents can be constructed for a


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better understanding of their current social interdependence. The direct engagement

relationship specifies the situation in which there is a direct engagement for which

the first agent is the client and the second agent is the server. In general, however, any

agent involved in an engagement chain engages all those agents that appear subse-

quently in the chain. To distinguish engagements involving an intermediate agent weintroduce the indirect engagement relation indengages; an agent indirectly engages

another if it engages it, but does notdirectlyengage it. If many agents directly engage

the same entity, then no single agent has complete control over it. It is important to

understandwhen the behaviour of an engaged entity can be modified without any

deleterious effect (such as when no other agent uses the entity for a different pur-

pose). In this case we say that the agent owns the entity. An agent, c, owns another

agent,s, if, for every sequence of server-agents in an engagement chain, ec, in which

sappears,c precedes it, orc is the autonomous client-agent that initiated the chain.

An agentdirectly owns another if it owns it and directly engages it. We can further

distinguish theuniquely ownsrelation, which holds when an agentdirectlyandsolely

owns another, andspecifically owns, which holds when it owns it, and has only one

goal. These definitions are presented below.

directly engages

c: Agent; s: ServerAgent (c, s) dengages d: dengagements d.client= c d.server= s

engages

c: Agent, s: ServerAgent (c, s) engages ec: engchains (s (ran ec.agentchain)

c= ec.AutonomousAgent)(((c, s), ec.agentchain) before)

indirectly engages

indengages= engages \ dengages

owns

c: Agent; s: ServerAgent (c, s) owns( ec: engchains| s ran ec.agentchain

ec.AutonomousAgent= c ((c, s), ec.agentchain) before)

directly owns

downs= owns dengages

uniquely owns


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c: Agent; s: ServerAgent (c, s) uowns(c, s) downs ( a: Agent| a =c (a, s) engages)

specifically owns

c: Agent; s: ServerAgent (c, s) sowns(c, s) owns #(s.goals) = 1

Thus the agent framework allows an explicit and precise analysis of multi-agent

systems with no more conceptual primitives than were introduced for the initial

framework to describe individual agents. Using these fundamental forms of inter-

action, we can proceed to define a more detailed taxonomy of inter-agent relation-

ships that allows a richer understanding of the social configuration of agents, sug-

gesting different possibilities for interaction, as shown by the relationships below,

taken from [20]. Importantly, the relationships identified are not imposed on multi-

agent systems, but arise naturally from agents interacting, and therefore underlie all

multi-agent systems.

1.5 Sociological Behaviour

Now, social behaviour involves an agent interacting with others; sociological be-

haviour requires more, that an agent understand its relationships with others. In order

to do so, it must model them, their relationships, and their plans.

1.5.1 Models and Plans

To model their environment, agents require an internal store, without which their

past experience could not influence direct behaviour, resulting in reflexive action

alone. A store exists as part of an agents state in an environment but it must also haveexistedpriorto that state. We call this feature aninternal storeormemory, and define

store agentsas those with memories. Unlike socialagents that engage in interaction

with others,sociologicalagents model relationships as well as agents. It is a simple

matter to define the model an agent has of another agent (AgentModel), by re-using

the agent framework components as shown below. Even though the types of these

constructs are equivalent to those presented earlier, it is useful to distinguish physical

constructs from mental constructs such as models, as it provides a conceptual aid. We

can similarly define models of other components and relationships so that specifying

a sociological agent amounts to a refinement of theAgentschema as outlined below.

EntityModel== EntityAgentModel== Agent

AutonomousAgentModel== AutonomousAgentCoopModel== Cooperation

EngModel== DirectEngagementChainModel== EngagementChain


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A sociological agent therefore views its environment as containing a collection

of entities with engagements, engagement chains and cooperations between them.

There are many consistency checks that need to be specified at this level, such as if a

sociological agent has a model of a direct engagement (say) then it must model both

those entities involved as having the goal of the direct engagement. However, thereare many details, and we omit then in our definition below.

ModelAgent ::=entEntity| objObject| agnAgent| aagAutonomousAgent

ModelRelationship::= chainChainModel| engEngModel| coopCoopModel

Model ::=relmodelModelRelationship| agentmodelModelRelationship

SociologicalAgentAutonomousAgentState

models: PModel

Now, in order to consider sociological agents with planning capabilities, we can

construct a high-level model ofplan-agents that applies equally well to reactive or

deliberative, single-agent or multi-agent, planners. It represents a high-level of ab-

straction without committing to the nature of an agent, the plan representation, or

of the agents environment; we simply distinguish categories of plan and possible

relationships between an agents plans and goals. Specifically, we defineactiveplans

as those identified as candidate plans not yet selected for execution; and executable

plans as those active plans that have been selected for execution.

Formally, we initially define the set of all agent plans to be a given set ([Plan]),so that at this stage we abstract out any information about the nature of plans them-

selves. Our highest-level description of a plan-agentcan then be formalised in the

PlanAgentschema below.

PlanAgent

Agent

goallibrary: P Goalplanlibrary, activeplans, executableplans: P Planactiveplangoal,plangoallibrary: Goal P Plan

dom activeplangoal goals (ran activeplangoal) =activeplans

domplangoallibrary goallibrary (ranplangoallibrary) planlibrary

goals goallibrary executableplans activeplans planlibrary


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SociologicalPlanAgent

SociologicalAgent

PlanAgent

The variables goallibrary, planlibrary, activeplans and executableplans repre-

sent the agents repository of goals, repository of plans, active plans and executable

plans, respectively. Each active plan is necessarily associated with one or more of

the agents current goals as specified by activeplangoal. For example, if the func-

tion contains the pair (g, {p1,p2,p3}), it indicates thatp1,p2 and p3 are competingactive plans for g. While active plans must be associated with at least one active

goal, the converse is not true, since agents may have goals for which no plans have

been considered. Analogously the plangoallibraryfunction relates the repository of

goals,goallibrary, to the repository of plans, planlibrary. However, not necessarily

all library plans and goals are related by this function.

1.5.2 Plan and Agent Categories

Now, using these notions, we can describe some example categories of goals, agents

and plans (with respect to the models of the sociological plan-agent), that may be

relevant to an agents understanding of its environment. Each of the categories is

formally defined below, where the sociological plan-agent is denoted as spa. Any

variable preceded bymodeldenotes the models that spahas of some specific type of

entity or relationship. For example,spa.modelneutralobjectsandspa.modelownsare

the neutral objects and ownership relations the sociological agent models.

self-suff plan

p spa.planlibrary selfsuff(p) spa.planentities(p)

spa.modelneutralobjects spa.modelselfspa.modelowns(|spa.modelself |)

self-suff goal

g spa.goallibrary selfsuffgoal(g)(p spa.plangoallibrary(g) p selfsuff)

reliant goal

g spa.goallibrary reliantgoal(g)spa.plangoallibrary g={ }

(p: spa.plangoallibrary g p selfsuff)

Aself-sufficient planis any plan that involves only neutral-objects, server-agentsthe plan-agent owns, and the plan-agent itself. Self-sufficient plans can therefore be

executed without regard to other agents, and exploit current agent relationships. (The

formal definition uses the relational image operator: in general, the relational image


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R(| S|)of a setSthrough a relation R is the set of all objectsy to whichR relates tosome memberx ofS.) A self-sufficient goalis any goal in the goal library that has an

associated self-sufficient plan. These goals can then, according to the agents model,

be achieved independently of the existing social configuration. Areliant-goalis any

goal that has a non-empty set of associated plans that is not self-sufficient.For each plan that is not self-sufficient, a sociological plan-agent can establish

the autonomous agents that may be affected by its execution, which is an important

criterion in selecting a plan from competing active plans. An autonomous agent A

may be affectedby a planin one of two ways: either it is required to perform an action

directly, or it is engaging a server-agent Srequired by the plan. In this latter case,

a sociological plan-agent can reason about either persuading A to share or release

S, taking Swithout permission, or finding an alternative server-agent or plan. To

facilitate such an analysis, we can define further categories of agents and plans, as

described in [20], but we do not consider them further here.

1.6 Autonomous Interaction as Motivated Discovery

Many traditional models of interaction have assumed an ideal world in which un-

founded assumptions have given rise to inadequate characterisations of interaction

amongst autonomous agents. If we consider autonomous interaction to be a process

of uncertain outcome (which it must be), then we can characterise it in a more gen-

eral way as a process ofdiscoveryin terms of the effects of actions. This allows us to

deal effectively with the inherent uncertainty in interaction. In this section, we show

how the ideas of discovery can be used to approach autonomous interaction. We be-

gin with an introduction to the ideas of discovery, and then show how they may be

applied and formalised in the multi-agent domain.

1.6.1 Motivated Discovery

Scientific discovery is a process that occurs in the real world. Many examples of

actual discovery have been observed and recorded, providing a basis for analyses of

the reasoning methods used by real scientists. This has led to the identification of

temporally and physically distinct elements in the discovery process which strongly

support the notion of discovery as a methodology for reasoning rather than a single

magical process. Moreover, the underlying motivation behind scientific reasoning

(and discovery) is one of increasing knowledge, understanding and awareness of

a natural external environment in order to be able to explain, predict and possibly

manipulate that environment. The second of these provides us with a large part of

what we want to achieve in AI to explain, predict and manipulate our environment.

The first, if the notion of a methodology for discovery is even partly correct, provides

us with a suitable means (in AI) for achieving it.In the context of autonomous interaction, agents behave according to a certain

understanding ortheoryof their environment and the agents within it, that we might

in a different context consider to be the models we have just described. In this section,


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we will refer to atheoryfor the sake of adopting thediscoverystance, but we might

equally be referring to these models of others, and of interaction itself.

We adopt Lucks simple but encompassing model for discovery [16] that entails

six stages, as follows.

1. Prediction:deductively generating predictions from a theory of interaction and a

scenario;

2. Experimentation:testing the predictions (and hence the theory of interaction) by

constructing appropriate experiments;

3. Observation:observing the results of experiments;

4. Evaluation:comparing and evaluating observations and predictions to determine

if the theory has been refuted;

5. Revision:revising the theory to account for anomalies; and

6. Selection:choosing the best resulting revised theory.

The framework is a cyclical one, repeating until stability is achieved with a con-

sistent theory. It begins with prediction which entails generating predictions for a

given scenario, and then subjecting these to some kind ofexperimentation. Throughobservationandevaluation, the results of the experiment are compared with the pre-

dictions and, in the event that they are consistent with each other, no action is neces-

sary. If the observations and predictions are anomalous, however, the theory must be

revised, and a suitable revision selectedto be passed through to the beginning of the

cycle for use in generating new predictions. Even when no failure occurs, the theory

is still liable to provide anomalies at a later stage.

Prediction

Perhaps the least troublesome part of the cycle is prediction. This is a simple deduc-

tive procedure that draws logical inferences from a theory and background knowl-

edge given a description of a particular scenario. In order to make sense of our envi-

ronment, we continually anticipate the effects of our actions, and of external factors

we make predictions about what will happen next. Usually, our predictions are

correct and we anticipate well, but there are instances when the predictions fail, and

we must deal with these failures later on in the cycle.

Generating predictions can be an expensive procedure, however, demanding time

and resources which may not be available. We might for example be able to predict

first, second and third places in an election, yet if we are only interested in who wins,

only one of the predictions needs to be generated. This is related to the motivations

of the reasoning agent, in the context of which the relevance of predictions can be

assessed.

Experimentation

Once predictions have been generated, they may be empirically tested, and the results

of these experiments can be compared with the predictions to determine if the theory

(or indeed background knowledge) is, as much as possible, correct and consistent.


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This implies a certain requirement on theories that has not yet been mentioned

that they be refutable, or falsifiable.

We can think of experimentation as being one of two kinds. First, there are ac-

tiveexperiments in which the experimenter carefully constructs apparatus, or forces

controlled environmental conditions with the aim of testing a particular character-istic or condition of a theory. Included in these are typical laboratory experiments.

Alternatively, and more commonly, there arepassiveexperiments which include any

situation for which an expectation is generated, but for which there is no explicit

theory. For example, squeezing a tube of toothpaste when brushing teeth is a pas-

sive experiment which has no controlled conditions, but which will determine if the

expectation of producing toothpaste is correct or not. Both of these are important.

When concerned with the problem of specifically acquiring knowledge in narrow

domains, active experiments are prevalent. In normal everyday affairs, passive ex-

periments are the norm unless they meet with a prediction failure. In this case, it is

typical to switch to active experiments to find the reason for the failure, if necessary.

In the case of autonomous interaction, any kind of act designed to elicit a response

can be regarded as an experiment.Thus experimentation is responsible for designing and constructing experiments

in order that imperfections in the theory may be detected and corrected.

Observation

We intend this to be a complete and encompassing framework. Were we to exclude

observation, it would not be so. Although observation immediately appears trans-

parently simple, requiring merely that changes in the environment be observed and

recorded for future reference, it is a little more complicated. (It should be noted that

observations may be forced by the use of controlled experiments, or may occur inde-

pendently.) Observations are compared with predictions and used to decide whether

the theory is acceptable, or whether it needs to be revised.

Ideally, we would want an independent observer, a system capable of perceiving

the external world, filtering out irrelevant information, and providing observations as

input to the reasoning system.

Evaluation

At this point, the experiment has been carried out, the observations have been

recorded, but it remains to decide whether or not the theory has been falsified,

whether or not it is acceptable. To make this decision, we need to be aware of a num-

ber of influential factors and to evaluate the evidence in this light. Principally, this is

concerned with the quality of the evidence. If an agent is to be effective, then it must

be able to cope with both experimental and observational error, and must be able

to evaluate them in an appropriate context. Little needs to be said about the occur-rence of errors, for it is undeniable that they are always present to some degree. It is,

however, unacceptable to pretend to cope with them by introducing simple tolerance

levels. Experimental evidence must be evaluated relative to the current motivations


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of a system, taking into account the implications of success or failure. In medical

domains, for example, even a small degree of error may be unacceptable if it would

lead to the loss of a patients life, while weather prediction systems may, in certain

circumstances, allow a far greater error tolerance.

Revision

If it is decided that the theory has been falsified, then it must be revised so that

it is consistent with the falsifying observations. Alternatively, new theories may be

introduced or generated by another reasoning technique such as analogy, case-based

reasoning, etc. The problem of creating new theories beyond direct observation is

outside of this framework. Yet we do allow for their introduction into the inductive

cycle, and in addition we allow for new theories based solely upon direct observation.

Revisions to the theory should include all those possible within the restrictions

of the knowledge representation used that are consistent with the observations. This

leads to the problem of combinatorial explosion, however, and the revision process

should therefore be additionally constrained by heuristic search, the search heuristicsbeing considered in the next and final stage. Allowing all revisions, potentially at

least, is important in order that they are not pre-judged out of context.

Selection

As mentioned above, this is not really a separate stage, and proceeds in tandem with

revision, but the task is distinct. Since the number of possible revisions to a given

theory is extremely large, there must be criteria for selecting those theories which

are better than others. Many criteria for rating theories have been proposed, such as

simplicity, predictive power, modesty, conservatism and corroboration.

However, selection of theories must be in context. This means that the goals

and motivations of a system are relevant to the task of judging which criteria aremore important in evaluating a theory. The way in which these criteria are applied

depends upon the context in which they are used and the need for which they are

used. For appropriateness of use in many situations, we may prefer Newtons laws to

Einsteins, but in other circumstances, only Einsteins may be acceptable.

1.6.2 Autonomous Interaction

In this subsection, we apply the framework just described to the problem of au-

tonomous interaction, reformulating the discovery concepts, and formalising the pro-

cess of interaction.

In order to make sense of our environment and to function effectively in it, we

continually anticipate the effects of our actions and utterances we make predic-tions (or expectations) about what will happen next. The action-selection function,

autoactions, of the AutonomousAgentActschema encompasses the deliberation of

the agent. The action that is selected is intended to satisfy the goals of the agent


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through its resulting effects and consequent changes to the environment. In the case

of an interaction episode involving two agents, the initiating agent selects an ac-

tion that is intended to cause the desired response in the responding agent. The

uncertainty inherent in such interaction means that the effects cannot be known in

advance, but can only be discovered after the event has taken place, or action per-formed. We describe this by specifying the predicted effects of actions selected in

theAutonomousAgentActschema by applying thesocialeffectinteractfunction to the

current view of the environment and those actions. The agent thus predicts that these

actions will change the environment to achieve the desired results. Remember that

the environment includes all of the entities in it, so that a change to an agent in the

environment will in turn cause a change to the environment itself. We also introduce

a variable to store an agents actual percepts prior to an operation,oldpercepts, which

will be used later in theDecideschema.

Lastly, remember that willdo, specifies the actions that are performed and not

the actions that the agent selects to perform next. In general, this is specified by the

variabletodowhich is a function of the agents motivations, goals and current view

of the environment (and not of the actual environment which dictates what actionsare actually performed). In successful operation willdoshould equaltodo. However,

when agents have only limited knowledge, perceptual capabilities or habiting dy-

namic open worlds these variables will not always equate. It is such anomalies that

signal to the agent that it must revise its current model of itself and environment.

SocialAgentPredict

SociologicalAgent

socialeffectinteract: View PAction Viewoldpercepts,prediction: Viewselectaction: PMotivation P Goal View PActiontodo: PAction

todo= selectaction motivations goals actualperceptsprediction= socialeffectinteract actualpercepts todoprediction

goals={}

In order to achieve the desired result, the relevant actions must be performed.

Effectively, this acts as an experiment, testing whether the predictions generated are

consistent with the resulting effects. In this sense, experimentation is central to this

model, for such interaction with the environment is the only way in which an agents

understanding of its capabilities and its environment can be assessed to bring to light

inadequacies, inconsistencies and errors. When an action is performed, it affects the

models of other agents and of the agent society which, after the change, are derived

from the previous models (of both the agents and inter-agent relationships) and the

view of the environment through the function,updatemodels. These models of agentsand their relationships are critical in determining if the action was successful.


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SocialAgentInteract

SocialAgentPredict

updatemodels: PModel View PModel

The action also has an effect on the environment, which changes accordingly, and

a similar effect on the agent itself whose percepts also change. For example, in the

case of an action which issues a request to another agent to tell the current time, the

resulting model will either encode the fact that the agent is telling the time, or not.

By inspecting this model and its attributes, the requesting agent can determine if its

action has been successful. Note that the new value ofoldperceptstakes the previous

value ofactualperceptsfor later use.

SocialEnv

SocialAgentPredict

SocialAgentInteract

env =effectinteract env willdoposspercepts =canperceive env perceivingactionsactualpercepts =willperceive motivations goals posspercepts

willdo =autoactions motivations goals actualpercepts env

models =updatemodels models actualpercepts

oldpercepts =actualperceptsprediction = prediction

Evaluating the results of the actions appears simple. At the most basic level, it in-

volves the comparison of predictions with observations. Thus if the intended effects

of the actions and the actual effects match, then the actions have achieved the desired

result and the episode is successful. If they are anomalous, then it reveals an erro-

neous understanding of the environment and the agents within it, or an inadequate

capability for perception of the results. The important point here is that there is no

guarantee of success, and failure can be due to any number of reasons.

This analysis assumes that the evidence is perfect, however, which may not al-

ways be appropriate. In any real environment this is not so, and error can be in-

troduced into evidence in a variety of ways, reducing the quality of the observed

evidence accordingly. Not only may there be inaccuracy due to the inherent uncer-

tainty in both performing the actions and perception of the results (experimentation

and observation respectively), but also, if the actions taken by the agent are commu-

nicative actions intended to elicit a response from another autonomous agent, then

there may be inaccuracy due to malicious intent on the part of the responding agent

by providing misleading information, for example [23]. Thus the response may itself

be the vessel for the error.

In addition to assessing the fit of observations with predictions, therefore, thequality of the observations themselves must also be assessed in order to ascertain

whether they are acceptable to be used in the comparison at all. Simple tolerance

levels for assessing the acceptability of perceived evidence are inadequate, for they


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do not consider the need for the interaction episode, and the importance of achiev-

ing the desired result. The quality demanded of the observations can thus only be

assessed in relation to the motivations of the agent which provide a measure of the

importance of the situation, and take into account the implications of success and

failure. In medical domains, for example, where the agents are highly motivated,even a small degree of error in interaction of relevant patient details may be unac-

ceptable if it would lead to the loss of a patients life, while neighbourly discussion

of the weather with low motivations and little importance may allow a far greater

error tolerance.

The schemas below describe evaluation with two predicates. The predicate

accept, holds between the capabilities of the agent, its perceived environment be-

fore and after the actions were performed, and the agent models, if the evidence

is acceptable. The capabilities of the agent capture the uncertainty information that

arises from the agent itself, while the perceived environment and agent models in-

clude details of difficulties arising through the environment, or other agents. The

considerpredicate compares predictions and observations once evidence is accepted.

Note that the potentially difficult question of when observations match predictions isbound up in the function itself which may be interpreted either as a simple equality

test or as something more sophisticated.

TheDecideschema also states at the beginning that though the agent changes as

a result of this evaluation (SocialAgent), the state of the agent remains the same

(AutonomousAgentState). Finally, if the evidence is accepted, and the observations

do not match the predictions, then the agent models must be revised as specified by

revisemodels.

bool::= True| False

SocialAgentEvaluate

accept : (PAction View View PModel)consider : P(View View)

Decide

SociologicalAgent

AutonomousAgentState

SocialAgentPredict

SocialAgentEvaluate

revisemodels : View PModel PModel

accept(capabilities, actualpercepts, oldpercepts,models) consider(prediction, actualpercepts)

models =revisemodels actualpercepts models


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1.7 Discussion

Our efforts with BDI agents [10, 9] have shown that formal computational models of

implemented systems and idealised systems, using the Z specification language [31],

a standard (and commonly-used) formal method of software engineering, can resultin implementations that are much more strongly related. In particular, they can be

checked for type-correctness, they can be animated to provide prototype systems, and

they can be formally and systematically refined to produce provably correct imple-

mentations. In this vein, related work has sought to contribute to the conceptual and

theoretical foundations of agent-based systems through the use of such specification

languages (used in traditional software engineering) that enable formal modelling

yet provide a basis for implementation of practical systems.

Indeed, as the fields of intelligent agents and multi-agent systems move relent-

lessly forwards, it is becoming increasingly more important to maintain a coherent

world view that both structures existing work and provides a base on which to keep

pace with the latest advances. Our framework has allowed us to do just that. By

elaborating the agent hierarchy in different ways, we have been able to detail bothindividual agent functionality and develop models of evolving social relationships

between agents with, for example, our analyses of goal generation and adoption, and

our treatment of engagement and cooperation. Not only does this provide a clear

conceptual foundation, it also allows us to refine our level of description to particular

systems and theories.

The problems with existing notions of agency and autonomy are now well-

understood, but the importance of these notions remains high, nevertheless. In pre-

vious work we have addressed this by constructing a formal specification to identify

and characterise those entities called agents and autonomous agents, in a precise yet

accessible way. Our taxonomy provides clear definitions for objects, agents and au-

tonomous agents that allow a better understanding of the functionality of different

systems. It explicates those factors that are necessary for agency and autonomy, and

is sufficiently abstract to cover the gamut of agents, both hardware and software,

intelligent and unintelligent.

Then, by taking autonomous interaction to be a process of discovery within the

framework, we can avoid the problems identified earlier ofguaranteed effects and

automatic intention recognition. In discovery, no effects are known for certain in

advance, but instead, (tentative) predictions or expectations of future states of the

world can be generated. It is only possible to be certain about effects once the actions

have been carried out. This can lead to a re-evaluation of existing models.

Additionally, we assert that the process of autonomous communication must

be motivated, and consequently a motivated agent does not have a pre-determined

agenda, nor is it benevolent. Motivations provide a means by which an agent can

set its own agenda, or set its own goals and determine which actions to perform in

achieving them. The effects of benevolent behaviour are possible, but only throughself-serving motivations. Moreover, because effects are not guaranteed, failure is al-

ways possible, but the combination of discovery and motivations allow effective ex-

ploitation of these failures and also recovery from them whenever possible.


28/30


Our aim in constructing the model for autonomous interaction is ambitious. We

are attempting to provide a common unifying framework within which different lev-

els of abstraction of reasoning, behavioural and interaction tasks can be related and

considered. We have necessarily concentrated on a high-level specification so that

the key principles can be explicated, but without sacrificing the need for precisenessthrough formality. By explicitly introducing motivated reasoning as part of the agent

framework, and providing the capacity for effectively dealing with dynamic worlds

through discovery, we provide a way in which the inadequacies in existing models

may be addressed.

A significant claim of this work is that it can provide a general mathematical

framework within which different models, and particular systems, can be defined

and contrasted. Z is particularly suitable in squaring the demands of formal mod-

elling with the need for implementation by allowing transition between specification

and program. There are many well-developed strategies and tools to aid this trans-

formation. Programs can also be verifiedwith respect to a specification; it is possible

to prove that a program behaves precisely as set out in the Z specification. This is not

possible when specifications are written in modal logics since they have the compu-tationally ungrounded possible-worlds model as their semantics. Thus our approach

to formal specification is pragmatic; we need to be formal to be precise about the

concepts we discuss, yet we want to remain directly connected to issues of imple-

mentation. We have also found the Z language is sufficiently expressive to allow a

consistent, unified and structured account of a computer system and its associated

operations.

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Formal Methods and Agent-Based Systems